Sheet product dispensers (e.g., napkin dispensers, paper towel dispensers, and tissue dispensers), provide on-demand sheet product to a user from a supply of sheet product stored within the dispenser. In some sheet product dispensers, a roll of sheet product is used. A roll of sheet product generally may include a web of sheet product that is wrapped around an axis such that numerous layers of the sheet product are wound around one another. The sheet product may be dispensed by manually or automatically rotating the roll to unwind a portion of the sheet product from the roll and then separating the desired portion from a remainder of the roll. The roll of sheet product may include a central opening extending therethrough along the axis of the roll. Certain rolls of sheet product may be coreless, such that the central opening of the roll is defined by an inner layer of the sheet product. Other rolls of sheet product may be cored, such that the central opening of the roll is defined by a core of paperboard or other material around which the layers of the sheet product are wound. Perforations or cutting arrangements may be used to separate the sheet product for use (e.g., to form a dispensed portion.